1. Field of the Invention
The present invention relates to an energy attenuating device, more particularly, the energy attenuating device is applied to a braking system.
2. Description of Related Art
Theoretically, induced electromotive force (EF) in a magnetic field is contributed by many intrinsic factors, for example, the ratio of two coil loops (stator, rotor), the strength of magnetic flux, the time rate of flux, and so on. In the magnetic field with high flux strength, the magnitude of attractive force between rotor and stator is extremely high and related to the above factors. The attractive force is well known as the “magnetic reluctance (MR)”.
For a braking system having a propeller and generators, after the magnetic coils such as wired coils on the rotor for the AC generator are excited, the magnetic reluctance force is so-called “braking effect”.
For braking purpose, the generator is driven by a propeller in the vehicle. If the vehicle is travelling at high speed, the angular velocity of the propeller is large. At this moment, the rate of magnetic flux also changes positively proportion to the angular velocity of the propeller. When a magnetic field coil of the rotor is provided with highly flux density, a slight rotation of the coil or a little flux change can induce a high electromotive force. That is, when other conditions are constantly fixed, the strength of the induced electromotive force changes in proportion to the rate of the flux change. Any circuit and component may be destroyed by the high induced electromotive force or voltage shock. Consequently, a problem accordingly occurs in the electrical-magnetic braking system. That is, the induced high electromotive force will cause a break down in the braking system
Up to now, the most commonly used solution for the voltage shock is to incorporate a voltage regulator into the braking system to regulate the magnitude of the current and to limit the current based on a pre-determined limiting threshold. The magnitude of the current in magnetic coil can be repressed so as to avoid the disaster resulted from the voltage shock. Hence, the magnetic reluctance force is also decreased, i.e. the braking force is dropped out.
In another solution for the high voltage shock, dissipating diodes are used as the dampers to consume the induced high electromotive force. Based on the concept of the energy transformation, the high speed vehicle is regarded as the vehicle with large kinetic energy. The braking of the high speed vehicle means the kinetic energy is transformed into heat or electrical energy. The temperature in the braking system increases very quickly so that a solution to absorb the heat effectively is necessary. Therefore, an additional air cooling or water cooling device has to be added into the braking system. In practice, many physical conditions should be considered, for instance, the space for mounting the cooling device, the safety and reliability of the cooling device, and so on. For example, a bus driver applies to braking just 3-5 seconds only when the brake petal is stepped on. Keeping the braking continuously is very difficult. For a high speed vehicle, the conventional braking system completely fails to carry out the braking task.
Theoretically, in the book of “K. L. Johnson; Contact Mechanics, Cambridge University Press., 1987, at pages 88-93, 96, 109, 120, 125, 248, 255, 279, 300”, a effective Young's module E* is defined as
                              1                      E            *                          =                                            1              -                              v                1                2                                                    E              1                                +                                    1              -                              v                2                2                                                    E              2                                                          (        1        )            
Another parameter km which is called mean curvature is defined as
                              k          m                =                                            1              2                        ⁢                          (                                                1                                      R                    ′                                                  +                                  1                                      R                    ′                                                              )                                =                                    1              2                        ⁢                          (                                                1                                      R                    1                                                  +                                  1                                      R                    2                                                              )                                                          (        2        )            
The contact size is related to the mean contact pressure Pm and mean curvature km as the following
                                          α            ∝                                          [                                                                            p                      m                                        ⁡                                          (                                                                        1                                                      E                            1                                                                          +                                                  1                                                      E                            2                                                                                              )                                                                            (                                                                  1                                                  R                          1                                                                    +                                              1                                                  R                          2                                                                                      )                                                  ]                                            1                3                                              =                                                    [                                                                            p                      m                                        ⁡                                          (                                                                        1                                                      E                            1                                                                          +                                                  1                                                      E                            2                                                                                              )                                                                            2                    ⁢                                          k                      m                                                                      ]                                            1                3                                      ⁢                                                  ⁢            or                          ⁢                                  ⁢                                            P              m                        ∝                                          [                                                                            p                      ⁡                                              (                                                                              1                                                          R                              1                                                                                +                                                      1                                                          R                              2                                                                                                      )                                                              2                                                                              (                                                                        1                                                      E                            1                                                                          +                                                  1                                                      E                            2                                                                                              )                                        2                                                  ]                                            1                3                                              =                                    [                                                                    p                    ⁡                                          (                                              2                        ⁢                                                  k                          m                                                                    )                                                        2                                                                      (                                                                  1                                                  E                          1                                                                    +                                              1                                                  E                          2                                                                                      )                                    2                                            ]                                      1              3                                                          (        3        )            
Based on the Hertz's solution for the point contact, we conclude that the following properties:
1. Contact size: a
                    a        =                              (                                          3                ⁢                PR                                            4                ⁢                                  E                  *                                                      )                                1            3                                              (        4        )            
2. Separation: δ
                    δ        =                                            a              2                        R                    =                                    (                                                9                  ⁢                                      P                    2                                                                    16                  ⁢                                                            R                      ⁡                                              (                                                  E                          *                                                )                                                              2                                                              )                                      1              3                                                          (        5        )            
3. Maximized normal stress: p0
                              p          0                =                                            3              ⁢              P                                      2              ⁢              π              ⁢                                                          ⁢                              a                2                                              =                                    (                                                6                  ⁢                                                            P                      ⁡                                              (                                                  E                          *                                                )                                                              2                                                                                        π                    3                                    ⁢                                      R                    2                                                              )                                      1              3                                                          (        6        )            
4. Maximized shear stress: □=0.57a
                              τ          max                =                              0.31            ⁢                          p              0                                =                                    0.47              ⁢                              P                                  π                  ⁢                                                                          ⁢                                      a                    2                                                                        =                                                            0.47                  ⁢                                      P                                          1                      3                                                                      π                            ⁢                                                (                                                            4                      ⁢                                              E                        *                                                                                    3                      ⁢                      R                                                        )                                                  2                  3                                                                                        (        7        )            
where P is the applied total normal force, R is equal to
  1      k    m  
5. For the tangential contact case, the β is defined as
                    β        =                                            1              2                        ⁡                          [                                                (                                                            1                      -                                              2                        ⁢                                                  v                          1                                                                                                            G                      1                                                        )                                -                                  (                                                            1                      -                                              2                        ⁢                                                  v                          2                                                                                                            G                      2                                                        )                                            ]                                /                      [                                          (                                                      1                    -                                          v                      1                                                                            G                    1                                                  )                            +                              (                                                      1                    -                                          v                      2                                                                            G                    2                                                  )                                                                        (        8        )            
Furthermore, the absolute value of □ is almost less than 0.25, this constant is related to the coefficient of friction. Referred to (1), the coefficient of friction □ is always smaller than
      β    5    ,      i    .    e    .  
                    0        <        •        ≤                  β          5                                    (        9        )            
If the material properties (tires, road) G1, G2, v1, v2 and weight of the vehicle are fixed, the friction force ƒ, at the contact patch never changes.
                              f          r                =                              •            ⁢                                                  ⁢            P                    ≤                                    β              ⁢                                                          ⁢              P                        5                                              (        10        )            
To see more details of the dynamic behaviors of braking system, refer to the thesis [P. W. Zegelaar. The dynamic response of types to brake torque variations and road univennesss Delft University of Technology., 1998]. By this way, with reference to equations (4), (5), (6) and (7), the contact size □ varied with magnitude of normal force is also a constant value. That is, the braking force is almost a constant value except from the numbers of tires and the weight of the vehicle increased. From the viewpoint of tribology (wear, friction and lubrication), a quite obvious limitation is that the braking force is not enough to block the high speed motion in the vehicle systems.
Some different kinds of design for eliminating the side effects of the bottleneck are required so as to elevate the safety of high speed vehicle and to provide the basic implementation issues of the energy recycling on braking. The voltage shock should be isolated and attenuated completely. In a sequel, the sharpness of kinetic energy relaxation process should not appear anymore.